Turn something on its head vs Turn something upside down

turn something on its head—(also: stand something on its head) cause a complete reversal of what is regarded as the norm:

• Suddenly, Jayne’s once sane life is turned on its head, and not even her closest friends are what they seem.

turn something upside down—

1. reverse smth. physically:

• Wolfe uncorked the bottle and turned it upside down. The water splashed the stones at Turrell’s feet.

2. = turn something on its head:

• That would have turned charity tax law upside down.

3. search everywhere in a place, especially roughly:

• The police turned his flat upside down looking for drugs.